A different, but related, scheme interprets the field as a probability
distribution, and treats the galaxies as points drawn from it in the
usual statistical sense. More specficially, this process can best be viewed as
a doubly-stochastic process, sometime called a Cox process.
The spatial dependence of the galaxy formation
is described by process 1, reflecting the evolution of
the initial density fluctuations into a formation
rate parameter in a probability distribution locally defined in space-time.
Process 2 represents the random sampling from the
rate determined by process 1. That is to say, the actual appearance
of a galaxy in the data is a second random process, independent of the first,
reflecting the appearance of a galaxy at a given point in space-time.
Indeed, one could separate the galaxy formation and observational detection
aspects into two separate, independent processes, if such a triply stochastic
representation should prove useful.
A mathematical introduction to the basics of such
random processes can be found in [1]}, and excellent overviews
of the mathematics of the corresponding theory and estimation methods are
[2]}, [3]}, [4]}, [5]}, [6]}, [7]}.
